On an identity with binomial coefficients (Q2313619)

In the present paper, a new identity associated with binomial coefficients is considered. This identity generates linear forms in the values of consecutive zeta constants generalizing the number-theoretic Apery-Beukers approach, which gives a chance to acquire novel algorithms for effectively evaluating of the Riemann zeta function at the integer points \(n\), \(n\geq 2\). The aim is to construct in the near future new fast algorithms for computing zeta constants on the basis of this approach.